# Shuffled Safe Codes

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

*Task 1 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group I), grades 9–11. The official answer and solution are in a separate file.*

In the Unsafe Vault there are four safes numbered 1, 2, 3, 4. The safes are not labelled, but the staff know which is which. The safes are fitted with electronic combination locks; a code consists of 4 digits, each of which is either 0 or 1. In the correct code, the position whose number equals the safe's number holds a one, and all the other positions hold zeros. For example, the code for safe number 3 is 0010. After the safes are closed, the electronic locks are connected to a server, which swaps the four existing codes around so that all 24 possible permutations are equally likely.

What is the probability that at least one safe gets its correct code again?

**Scoring criterion:** exact match of the answer — 12 points

**Maximum score for the task — 12**